It is shown that two vectors with coordinates in the finite q-element field of characteristic p belong to same orbit under natural action symmetric group if each elementary polynomials degree pk,2pk,…,(q−1)pk, k=0,1,2,… has value on them. This separating set polynomial invariants for permutation representation not far from being minimal when q=p and dimension large compared p. A relatively smal...

This work initiates the study of orthogonal symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach relies on previous work by the authors in which eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland Hamiltonian were construct...

Unitary matrices have a rich mathematicalstructure which is closely analogous to real symmetric matrices. For real symmetric matrices this structure can be exploited to develop very eecient numerical algorithms and for some of these algorithms unitary analogues are known. Here we present a unitary analogue of the bisection method for symmetric tridiagonal matrices. Recently Delsarte and Genin i...